數(shù)值分析方法知到智慧樹章節(jié)測試課后答案2024年秋浙江大學(xué)

數(shù)值分析方法知到智慧樹章節(jié)測試課后答案2024年秋浙江大學(xué)第一章單元測試

Whentheerrorpropagationformulais,itiscalledexponentialerrorpropagation.()

A:錯B:對

答案:錯Whenperforming（）operationwithtwosimilarnumbers,itiseasytocauselargererrors.（

A:Subtraction

B:Division

C:Multiplication

D:Addition

答案:Subtraction

Whichproblemsshouldbesolvedbynumericalanalyticaltool()?

A:

B:

C:

D:

答案:

；

Ifp*=10.001isanapproximateofp=10.000,thentherelativeerroris()

A:

B:

C:

D:

答案:

Toapproach1/3,weshoulduseatleast()significantdigitstoguaranteearelativeerrorof

A:

B:

C:

D:

答案:

第二章單元測試

Supposeisasequencethatconvergestop,withforalln.Ifpositiveconstantsandexistwith

.

Then,if,thesequenceislinearlyconvergent.()

A:錯B:對

答案:對Theconvergencerateofthebisectionmethodis（）.

A:

B:

C:

D:

答案:

TheconvergencerateoftheNewton’smethodis（）.

A:

B:

C:

D:

答案:

Letand.UseNewton’smethodtofind.canbeusedasaninitialpoint?（）

A:錯B:對

答案:錯Thefixed-pointproblemg(x)=x-x3-4x2+10cannotconvergeforinitialpointx0=1.5.（）

A:錯B:對

答案:對

第三章單元測試

IfavectorsequenceconvergestoXintheL1norm,italsoconvergestoXinthenorm.（）

A:對B:錯

答案:對Asufficientconditionfortheexistenceofauniquefixedpointiswithinagiveninterval.（）

A:錯B:對

答案:錯Whentheinitialvalueisincorrectlyselected,bothfixed-pointiterationandNewton’smethodwillfailtoconverge.（）

A:錯B:對

答案:對Beginningwith,theseconditerationofNewton’smethodfortheequationis0.6860.()

A:對B:錯

答案:對Theconvergencerateofthefixed-pointiterativemethodis（）.

A:

B:

C:

D:

答案:

第四章單元測試

IfAissymmetric,then.（）

A:錯B:對

答案:對Giventhelinearsystem

TheGauss-Seidelalgorithmcanbeusedtosolvethesystem.()

A:對B:錯

答案:對IfthespectralradiusofamatrixAsatisfies,thenAisaconvergentmatrix.()

A:錯B:對

答案:對Theiterativecalculationformulaforlinearproblemsis,theiterativeprocesscanconvergewhenTsatisfieswhichofthefollowingconditions?（）

A:ThespectralradiusofTislessthan1.

B:nislargeenough,theL2normofissmallenough

C:Tisaconvergentmatrix

D:nislargeenough,theL1normofissmallenough

答案:ThespectralradiusofTislessthan1.

；nislargeenough,theL2normofissmallenough

；Tisaconvergentmatrix

；nislargeenough,theL1normofissmallenough

Fortheiterativesolutionoflinearproblems,theJacobialgorithmalwaysconvergefasterthantheGauss-Seidelalgorithm.（）

A:錯B:對

答案:錯

第五章單元測試

Passingnpoints,apolynomialwithdegreenomorethannthatsatisfiestheinterpolationconditionsexistsandisunique.（）

A:錯B:對

答案:錯Whichofthefollowingstatementsarecorrectaboutpolynomialfitting?（）

A:Oneoftheadvantagesofpolynomialfittingisthatthealgebraicoperationsofpolynomialsarestillpolynomials

B:Thepolynomialwiththehighestdegreen-1whichpassthroughngivenpointsisunique

C:Taylorpolynomialscanonlyapproximateafunctionatacertainpoint

D:Inaclosedinterval,thereisnopolynomialfunctiontoapproximatetheexponentialfunctionwithsufficientprecision

答案:Oneoftheadvantagesofpolynomialfittingisthatthealgebraicoperationsofpolynomialsarestillpolynomials

；Thepolynomialwiththehighestdegreen-1whichpassthroughngivenpointsisunique

；Taylorpolynomialscanonlyapproximateafunctionatacertainpoint

Letbetheinterpolationpolynomialforthedata(0,0),(0.5,y),(1,3),and(2,2).Thecoefficientofinis6.Theny=4.25.()

A:對B:錯

答案:對ConstructtheLagrangeinterpolatingpolynomialofdegree2forthegivenvaluesofxandy:

Theny=6.712whenx=4.8.()

A:對B:錯

答案:對WritethelinearLagrangeinterpolatingpolynomialthatpassesthroughthepoints(2;4)and(5;1).Thenf(7)={2}.()

A:錯B:對

答案:錯Thegoalofleastsquaresapproximationminimizesthe（）normoftheerror.()

A:

B:

C:

D:

答案:

第六章單元測試

Theerrorofthethree-pointnumericaldifferentiationmethodis（）。

A:

B:

C:

D:

答案:

Whenconsideringtheroundingerror,boththefive-pointandthree-pointnumericaldifferentiationmethodshavethesameoptimalsteplengthh.()

A:錯B:對

答案:錯Theerrorofthefive-pointnumericaldifferentiationmethodis（）。

A:

B:

C:

D:

答案:

Whenconsideringtheroundingerror,thelargertheh,thehighertheprecisionofthenumericaldifferentiation.（）

A:錯B:對

答案:錯UsingRichardson'sextrapolationmethod,low-orderformulascanbeusedtoderivehigh-orderformulasforsolvingnumericaldifferentials.（）

A:對B:錯

答案:對

第七章單元測試

Theerrororderofthetrapezoidalintegralformulais（）。

A:

B:

C:

D:

答案:

Theerrororderofthecompositetrapezoidalintegralformulais（）.

A:

B:

C:

D:

答案:

TheSimpson’srulehasadegreeofprecision2.()

A:錯B:對

答案:錯RombergintegralistheapplicationofRichardsonextrapolationinnumericalintegration.()

A:對B:錯

答案:對Thequadratureformulaisexactforallpolynomialsofdegreelessthanorequalto2.Then,c0=1/3,c1=4/3,c2=1/3.()

A:對B:錯

答案:對

第八章單元測試

WhichofthefollowingfunctionsarenotLipschitzcontinuouson[0,1]?（）。

A:

B:

C:

D:

答案:

；

ThelocaltruncationerrorofEuler'smethodis（）.

A:

B:

C:

D:

答案: